Have you verified that your backup is a valid backup? That your files are there and you can recover them from the backup? If so, before you discard your old computer, you could try booting into Safe Mode (hold shift key on startup, it takes a long time to boot into Safe Mode). Then reboot normally, test for anomalous behavior. If it is still there, boot into Recovery (COMMAND-R) and run Disk Utility to repair the disk (first aid).
If the problems are still there, boot into Recovery again and erase/format the internal drive and do a fresh install of the Mac OS. Do this ONLY if you a good backup, preferably two good backups (make a second one if you can). After reinstalling the MacOS, reboot and migrate over only your user accounts and user files from the backup. Then install only new versions of the applications that you need. After each install, reboot and test for any anomalous behavior. If the Mac is still behaving badly, it probably has a hardware problem and getting a new Mac might make sense. If you get a new Mac, it will come with Big Sur and if the backup is sound, you should be able to migrate your user accounts and files to the new Mac. Very old versions of Microsoft Office no longer work under Catalina or Big Sur so you will need to acquire the newest versions.
